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PVD

PVD[r,n1,n2,n3,s1,s2,s3,s4,s12,s23,m0,m1,m2,m3]
is the Passarino-Veltman coefficient function .

Details and OptionsDetails and Options

  • PVD[r,n1,n2,n3,s1,s2,s3,s4,s12,s23,m0,m1,m2,m3] is the symbolic form of the coefficient function multiplying the symmetrized tensor generated by LoopIntegrate.
  • PVD[r,n1,n2,n3,s1,s2,s3,s4,s12,s23,m0,m1,m2,m3] implicitly depends on the number of spacetime dimensions .
  • PVD[0,0,0,0,s1,s2,s3,s4,s12,s23,m0,m1,m2,m3] represents the scalar function with full dependence on .
  • PVD does not automatically reorganize its arguments.
  • PVD does not directly evaluate. LoopRefine substitutes PVD with its explicit expression.
  • PVD[r,n1,n2,n3,s1,s2,s3,s4,s12,s23,m0,m1,m2,m3,Weights{w0,w1,w2,w3}] represents the weighted coefficient function .
  • PVD[r,n1,n2,n3,s1,s2,s3,s4,s12,s23,m0,m1,m2,m3,Dimensionsn] represents the coefficient function in spacetime dimensions.
  • The following are equal to PVD[r,n1,n2,n3,s1,s2,s3,s4,s12,s23,m0,m1,m2,m3] in other packages:
  • FeynCalcPaVe[,{s1,s2,s3,s4,s12,s23},{,,,}]
    LoopTools (IR finite and , )D0i[dd,s1,s2,s3,s4,s12,s23,,,,]

ExamplesExamplesopen allclose all

Basic Examples  (5)Basic Examples  (5)

Apply LoopRefine to substitute the analytic form of PVD:

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Weighted PVD:

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Taylor series expansion around :

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View PVD in TraditionalForm:

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TAdjustmentBox[E, BoxBaselineShift -> 0.5, BoxMargins -> {{-0.3, 0}, {0, 0}}]X code:

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More general cases are given in terms of ScalarD0:

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Apply D0Expand to obtain an expression in terms of more elementary functions:

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